86,805 research outputs found
Properties of Design-Based Functional Principal Components Analysis
This work aims at performing Functional Principal Components Analysis (FPCA)
with Horvitz-Thompson estimators when the observations are curves collected
with survey sampling techniques. One important motivation for this study is
that FPCA is a dimension reduction tool which is the first step to develop
model assisted approaches that can take auxiliary information into account.
FPCA relies on the estimation of the eigenelements of the covariance operator
which can be seen as nonlinear functionals. Adapting to our functional context
the linearization technique based on the influence function developed by
Deville (1999), we prove that these estimators are asymptotically design
unbiased and consistent. Under mild assumptions, asymptotic variances are
derived for the FPCA' estimators and consistent estimators of them are
proposed. Our approach is illustrated with a simulation study and we check the
good properties of the proposed estimators of the eigenelements as well as
their variance estimators obtained with the linearization approach.Comment: Revised version for J. of Statistical Planning and Inference (January
2009
An elementary way to rigorously estimate convergence to equilibrium and escape rates
We show an elementary method to have (finite time and asymptotic) computer
assisted explicit upper bounds on convergence to equilibrium (decay of
correlations) and escape rate for systems satisfying a Lasota Yorke inequality.
The bounds are deduced by the ones of suitable approximations of the system's
transfer operator. We also present some rigorous experiment showing the
approach and some concrete result.Comment: 14 pages, 6 figure
Adaptive finite element method assisted by stochastic simulation of chemical systems
Stochastic models of chemical systems are often analysed by solving the corresponding\ud
Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability\ud
distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density
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